Variation in the phase of response to low-frequency pure tones in the guinea pig auditory nerve as functions of stimulus level and frequency.

Abstract

The directionality of hair cell stimulation combined with the vibration of the basilar membrane causes the auditory nerve fiber action potentials, in response to low-frequency stimuli, to occur at a particular phase of the stimulus waveform. Because direct mechanical measurements at the cochlear apex are difficult, such phase locking has often been used to indirectly infer the basilar membrane motion. Here, we confirm and extend earlier data from mammals using sine wave stimulation over a wide range of sound levels (up to 90 dB sound pressure level). We recorded phase-locked responses to pure tones over a wide range of frequencies and sound levels of a large population of auditory nerve fibers in the anesthetized guinea pig. The results indicate that, for a constant frequency of stimulation, the phase lag decreases with increases in the characteristic frequency (CF) of the nerve fiber. The phase lag decreases up to a CF above the stimulation frequency, beyond which it decreases at a much slower rate. Such phase changes are consistent with known basal cochlear mechanics. Measurements from individual fibers showed smaller but systematic variations in phase with sound level, confirming previous reports. We found a "null" stimulation frequency at which little variation in phase occurred with sound level. This null frequency was often not at the CF. At stimulation frequencies below the null, there was a progressive lag with sound level and a progressive lead for stimulation frequencies above the null. This was maximally 0.2 cycles.

A The frequency response area as a grayscale plot. The CF of this fiber was 0.717 kHz and its spontaneous rate was 58.5 spikes/s. The sound levels are shown as attenuations: The mean maximum sound level over the range of this response area was 91 dB SPL with a standard deviation of 1.7 dB. B The variation of the compensated phase of phase locking as a function of stimulus frequency and sound level (compensated by subtracting the best fitting linear function to the phase curve measured from the FRA derived data at 79 dB SPL). C Period histograms from 50 repeats of tones at half-octave intervals (frequencies across the top, sound levels in dB SPL at the right). D The variation of raw phase values obtained from the histograms in C after unwrapping the phase. E The mean discharge rate as a function of the level and frequency of pure tones (frequency response area). F. The unwrapped raw phase data obtained from period histograms computed from the same data as E. Symbols used in B and D–F represent data for sound levels from 9–89 dB SPL as indicated in the key next to C. The arrow in A, B, and E indicated the frequency of the peak at the lowest sound level in E.

A Difference between two estimates of CF in octaves as a function of the mean of those estimates. B Histogram of the difference measure pooled across CF. The CF measures were estimated by (a) the audiovisual threshold during the experiment and (b) the peak of the frequency response function (e.g., Fig. E) at the lowest level presented.

Pooled plots of the variation of raw phase lag against CF in which the phase values at all sound levels measured are overplotted (note, there is no added shift in this figure, unlike Figs. and ). The frequencies displayed are at one quarter octave intervals starting at 250 Hz (250, 353, 500, 707, 1,000, 1,414, and 2,000 Hz). The top black symbols represent the 250-Hz data and the bottom black symbols represent the 2000-Hz data. The triangles indicate the stimulus frequency for the different plots and are placed by eye at the middle of the appropriate data and given the contrasting color.

Variation in phase of phase locking as a function of the fiber CF and the sound level. The curves for the different sound levels in each panel have been offset by one cycle and alternated shading for clarity. Each panel represents a different stimulus frequency. The vertical lines indicate the stimulus frequency. “Broken stick” fits are overplotted (see “” for details).

Variation of the knee-point and low-frequency slope with sound level and stimulus frequency. The data points were obtained by fitting a broken stick (two linear parts) to the data shown in three of the panels in Figure and extracting the parameters of the fit. A Position of the knee point for three stimulus frequencies (legend) as a function of sound level. The knee-point CF is expressed in octaves with respect to the stimulus frequency so that all three frequencies could be conveniently represented. B Slope of the low-CF part of the phase versus CF plot expressed in cycles/octave as a function of sound level.

Distribution of discharge rate across the fiber array for stimuli of four different frequencies (across the top) and six sound levels (in dB SPL as shown at the right). Each point is from a different fiber plotted at its CF. The rate has been normalized by subtracting the spontaneous rate and expressing it as a proportion of the maximum driven rate.

A Raw phase lag versus stimulus frequency curves for nine fibers at the highest sound level presented (approximately 90 dB SPL). B Delay to the recording site computed as the slope of the raw phase-frequency plots (as in A), plotted as a function of fiber characteristic frequency and sound level (in dB SPL as shown to the right). The y-axis is correct for the 40-dB SPL data and each subsequent plot is displaced by 5 ms for clarity. The open symbols are from a previous study in guinea pig (Palmer and Russell ). The solid line is the equation 87.56 × CF(Hz)−0.486 described in Figure 7 of Siegel et al. ().

A, C, E show the mean discharge rate of three fibers as a function of the stimulus frequency and sound level (FRA; as in Fig. B). The arrows indicate the frequency at which a peak occurred at the lowest sound level. B, D, F show the corrected phase of phase locking as a function of stimulus frequency and sound level derived from the data in A, C, and E. The data were corrected by subtracting the linear regression fit to the phase data derived from the highest level FRA. The thick arrows show the on-line audiovisual estimate of CF while the thin arrows show the frequency of the peaks at the lowest level in the FRA (A, C, E). Symbols used for different sound levels apply to both parts of the figure for each of the three fibers. The large symbols represent phase values obtained from period histograms after 50 stimulus repeats (see Fig. C, D). CFs and spontaneous rates of the fibers were A 0.407 kHz, 140 spikes/s; C 0.222 kHz, 49.5 spikes/s; and E 0.849 kHz, 58.6 spikes/s. Sound levels are shown in the key.

Offset of the null frequency (see text for explanation) from the CF as a function of the CF. The bar graph to the right shows the distribution of offsets collapsed across CF. The bar graph at the top shows the distribution of CFs sampled (in half-octave bands).

Offset of the null frequency from: left column, the audiovisually measured CF, and middle column, the BF estimated from the FRA measured at the lowest SPL tested. The right column shows a comparison of these two offsets. The top three rows show the data from three individual animals (the number in the right hand column is the animal ID#); the fourth row shows the data for all animals pooled.

Variation of the compensated phase as a function of CF for four stimulus frequencies (above each panel) and six sound levels (in dB SPL as shown in each panel). The data at different sound levels have been offset by 0.5 cycles. The data for the same three animals as shown in Figure , from which most fibers were isolated, are highlighted by different symbols (squares and upward and downward triangles) and the data for the remaining animals are plotted as solid circles. The horizontal lines provide a zero-phase reference for each sound level. The vertical lines indicate the stimulus frequency.